Pmsm compound sliding mode disturbance-observer-based control method with fusion parameter optimization

Abstract

This invention discloses a PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization, specifically including the following steps: Step 1, establishing a mathematical model of the permanent magnet synchronous motor; Step 2, constructing a cascaded finite-time phase-locked observer, i.e., a cascaded FT-PLLO; Step 3, constructing a calculus-integral sliding mode controller; Step 4, constructing a PSO-LSTM neural network optimization model; Step 5, traversing and optimizing the observer bandwidth and controller bandwidth through the PSO-LSTM neural network, inputting the optimized observer bandwidth into the cascaded FT-PLLO, and inputting the optimized controller bandwidth into the calculus-integral sliding mode controller to achieve control of the permanent magnet synchronous motor. This solves the problems of large speed fluctuations, long transient response times, and the dependence of observer and controller bandwidths on manual tuning in existing permanent magnet synchronous motor control methods during load changes.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control technology, and relates to a PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) offer advantages such as high power density, high efficiency, low torque ripple, and fast dynamic response, making them widely used in new energy vehicles, robots, servo drives, aerospace electric propulsion, and power electronic equipment. However, in actual operation, PMSMs are often affected by sudden load changes, parameter perturbations, external disturbances, inverter non-ideal factors, and sampling noise, leading to speed fluctuations, electromagnetic torque overshoot, and prolonged response time, thus impacting system stability and control accuracy.

[0003] Currently, commonly used control methods in the speed loop control of permanent magnet synchronous motors include PI control, Active Disturbance Rejection Control (ADRC), sliding mode control, and their improved versions. Traditional PI control is simple in structure and easy to implement in engineering, but its dynamic response capability is insufficient under sudden load increases or decreases, easily leading to problems such as speed drops and long recovery times. Traditional sliding mode control has strong robustness, but it is prone to chattering in engineering applications, and the control parameter tuning relies on experience. Traditional ADRC estimates the total system disturbance using an Extended State Observer (ESO), which can improve disturbance rejection capability; however, its observer bandwidth and controller bandwidth are usually manually tuned, making it difficult to simultaneously achieve speed, stability, and robustness under complex load disturbance conditions.

[0004] In recent years, intelligent algorithms such as neural networks and particle swarm optimization have been used for motor control parameter tuning. However, existing intelligent optimization methods are mostly used for PID parameter tuning or fault diagnosis, and research on the coordinated optimization of observer bandwidth and controller bandwidth in PMSM speed control and its combination with sliding mode control and finite-time disturbance observers is still insufficient. Summary of the Invention

[0005] The purpose of this invention is to provide a PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization, which solves the problems of large speed fluctuations, long transient response times, and the dependence of observer and controller bandwidth on manual tuning in existing permanent magnet synchronous motor control methods when the load changes abruptly.

[0006] The technical solution adopted in this invention is a PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization, which specifically includes the following steps: Step 1: Establish a mathematical model for the permanent magnet synchronous motor; Step 2: Construct a cascaded finite-time phase-locked observer, i.e., a cascaded FT-PLLO; Step 3: Construct a calculus sliding mode controller; Step 4: Construct the PSO-LSTM neural network optimization model; Step 5: The observer bandwidth and controller bandwidth are traversed and optimized by the PSO-LSTM neural network. The optimized observer bandwidth is input into the cascaded FT-PLLO, and the optimized controller bandwidth is input into the calculus-integral sliding mode controller to realize the control of the permanent magnet synchronous motor.

[0007] The invention is further characterized by: The specific process of step 1 is as follows: After Clark and Park transformations, the stator voltage equation of the PMSM in the synchronous rotating coordinate system is: (1) In the formula, u od and u oq These are the stator voltages of the PMSM respectively. d , q Axial components; i od and i oq For PMSM stator current d , q Axial components; R d and R q for d , q Shaft stator resistance; L d and L q for d , q Shaft stator inductance, for surface-mount PMSM, L d and L q They are equal in numerical value; oh e Electric angular velocity; ψ f For permanent magnet flux linkage; The equations of motion and electromagnetic torque of the PMSM are as follows: (2) In the formula, T e The electromagnetic torque of the PMSM;T l This is the load torque; B The coefficient of friction; J It is the moment of inertia; p n is the number of pole pairs of the PMSM; oh m This refers to the mechanical angular velocity.

[0008] The specific process of step 2 is as follows: Step 2.1, establish the primary structure of FT-PLLO; Step 2.2: Based on the first-level structure of FT-PLLO established in Step 2.1, design the second-level structure, namely the nonlinear FT-PLLO.

[0009] The specific process of step 2.1 is as follows: First, the internal and external disturbances of the system are separated and included in the total disturbance of the system. The corresponding standard first-order active disturbance rejection paradigm is: (3) In the formula, y o This is the system output; u For control input; b 0 represents the controller gain; F v This is the sum of the internal and external disturbances of the separated system; Equation (2) is fitted to the standard first-order active disturbance rejection paradigm as follows: (4) In the formula, i oq(ref) For PMSM q Reference value for the inner loop of shaft current; Define the state variables of the control system as follows: x 1= oh m ; x 2= F v Based on the defined state variables, the state-space equation is: (5) In the formula, the total internal and external disturbances F v The specific form is: (6) Based on the state-space equation of the system established by equation (5), the first-level structure of the cascaded FT-PLLO can be designed, that is, the form of the linear PLLO is: (7) In the formula, e 11 The observation error is for the first-order linear PLLO. r 11 , r 12 For each linear PLLO, the system state variables are... x 1. x 2 observations; x 11 , x 12 This is the gain coefficient of the linear PLLO.

[0010] The specific process of step 2.2 is as follows: Based on the first-level structure of the FT-PLLO established by equation (7), a second-level structure, namely the nonlinear FT-PLLO, is designed, with the following specific form: (8) In the formula, e 21 This represents the observation error of the second-order nonlinear FT-PLLO; r 21 , r 22 For FT-PLLO, the system state variables are respectively x 1. x 2 observations; x 21 , x 22 tanh is the gain coefficient of FT-PLLO; x ) is the hyperbolic tangent function; 0 < α <1.

[0011] The specific process of step 3 is as follows: The input error of the sliding mode controller in the PMSM speed loop is defined as: (9) In the formula, oh m(ref) This is a reference value for the mechanical angular velocity of the PMSM; r 21 This represents the final observed mechanical angular velocity from the cascaded FT-PLLO. Based on the input error of the defined controller, a fractional-order absolute exponential calculus sliding surface is designed. First, the fractional-order formula is introduced as follows: (10) In the formula, c Let be the order of the fractional differential operator; l and h These are the lower and upper limits of the fractional integral operator, respectively; Re( c )for c The real part, and c The sign of the real part determines the function f ( t ) is a fractional derivative or fractional integral, when c When the real part is 0, the function f ( t () is of integer order; According to the defined fractional order theory, assuming c Given a real number that is always positive, it is introduced into the designed original sliding surface to form a fractional-order absolute exponential calculus sliding surface, specifically in the form of: (11) In the formula, e ω Input the rotational speed error for the designed sliding surface; c 1. c 2 represents the sliding surface coefficient; m The design exponent is the absolute exponent term, and 0 < m <1.

[0012] In step 3, after calculating the first derivative of the designed sliding surface, the derivative is set to zero, and the equivalent control law of the sliding controller is obtained as follows: (12) Based on the designed fractional-order absolute exponential calculus sliding surface, a variable-parameter double-power error reaching law is introduced, specifically in the form of: (13) In the formula, k1 and k2 are the design parameters of the variable parameter double power error approach law, where k1 is greater than 0 and k2 is greater than 1.5; , To improve the high-frequency chattering suppression parameters of the reaching law, and , All are greater than 0; erf(x) is the error function in the probability distribution, specifically in the form of: (14) Based on the designed variable-parameter double-power error-reaching law, the specific form of the switching control law in the controller is as follows: (15) According to equations (12) and (15), the overall control law in the PMSM controller is: (16).

[0013] The specific process of step 4 is as follows: Step 4.1, establish the mathematical model of LSTM, specifically as follows: (17) In the formula, f t , i t , c t , u t , o t and h t These are the forget gate, input gate, candidate state, update unit state, output gate, and hidden state output of the LSTM neural network. x t The input vector; h t It is in a hidden state; b f , b i , b c , b o For the offset of the corresponding gate; W f , W i , W c and W o tanh( ) is the weighting coefficient; x ) is the hyperbolic tangent activation function; Step 4.2: Optimize the hyperparameters or output parameters of the LSTM neural network using the Particle Swarm Optimization (PSO) algorithm to obtain the PSO-LSTM neural network parameter optimization model.

[0014] The specific process of step 4.2 is as follows: The specific form of the velocity update expression in the particle state is: (18) In the formula, i Refers to the first i One particle; v i t For the first i The velocity vector of a particle in space; t This represents the number of iterations in the particle swarm optimization algorithm. oh Inertial weight; c 1. c 2 represents individual and social learning factors, respectively; r 1. r 2. Random numbers sampled independently in each dimension, ranging from [0,1];P tl The target position for a particle as it traverses space; G tl The target positions for all randomly generated particles to traverse in space; x i t Let be the position vector of a particle in space, specifically in the form of: (19) In the formula, x i t+1 For a certain particle in space relative x i t The position vector for the next iteration; Constraint factors; In the oh This inertia factor introduces linear decay, specifically in the form of: (20) In the formula, D This represents the total number of iterations in the particle swarm optimization algorithm. d This represents the current iteration number; oh max This represents the maximum value of the inertia weight. oh min This represents the minimum inertial weight.

[0015] The beneficial effects of this invention are that it proposes a PMSM composite sliding mode active disturbance rejection control strategy based on a PSO-LSTM neural network and applies it to the PMSM speed loop. First, a cascaded finite-time phase-locked loop observer (FT-PLLO) is designed to improve the system's observation accuracy of total internal and external disturbances. The controller part is designed with a fractional-order absolute exponential calculus sliding surface and introduces a variable-parameter double-power error reaching law, which significantly suppresses high-frequency chattering during sliding mode motion. Finally, a PSO-LSTM neural network is used to optimize some parameters in the SM-ADRC to fully utilize the controller's performance. Attached Figure Description

[0016] Figure 1 This is the main topology of the PMSM circuit in the PMSM composite sliding mode active disturbance rejection control method that integrates parameter optimization according to the present invention; Figure 2 This is a block diagram of the cascaded FT-PLLO structure of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention; Figure 3This is a block diagram of the controller part of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization according to the present invention. Figure 4 This is a block diagram of the LSTM neural network unit structure of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention; Figure 5(a) is a random scatter plot of the PSO effect before optimization in the PMSM composite sliding mode active disturbance rejection control method with fusion parameter optimization of the present invention. Figure 5(b) is a random scatter plot of the PSO optimization effect in the PMSM composite sliding mode active disturbance rejection control method with fusion parameter optimization of the present invention. Figure 6 This is a flowchart of the PSO-optimized LSTM neural network algorithm in the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention; Figure 7(a) is a speed waveform diagram of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization in this invention when the load changes abruptly. Figure 7(b) is a simulation waveform of the rotational speed during the sudden load change at point A in Figure 7(a); Figure 7(c) is a simulation waveform of the rotational speed during the sudden load change at point B in Figure 7(a); Figure 8(a) is a simulation waveform of electromagnetic torque during load change in the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention. Figure 8(b) is a simulation waveform of electromagnetic torque during the transient process at point A in Figure 8(a) when the load changes abruptly. Figure 8(c) is a simulation waveform of electromagnetic torque during the transient process at point B in Figure 8(a) when the load changes abruptly. Figure 9 This is a hardware-in-the-loop experimental principle block diagram used in the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention; Figure 10(a) shows the experimental results of speed and electromagnetic torque under conventional PI control when the load changes abruptly. Figure 10(b) shows the experimental results of speed and electromagnetic torque under conventional ADRC control when the load changes abruptly. Figure 10(c) shows the experimental results of rotational speed and electromagnetic torque under the control of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization according to the present invention, when the load changes abruptly. Figure 11(a) shows the experimental results of the stator three-phase current under conventional PI control when the load changes abruptly. Figure 11(b) shows the experimental results of the stator three-phase current under conventional ADRC control when the load changes abruptly. Figure 11(c) shows the experimental results of the stator three-phase current under the control of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization according to the present invention, when the load changes abruptly. Detailed Implementation

[0017] The following detailed description is provided in conjunction with specific implementation methods.

[0018] Example 1 The present invention integrates a PMSM composite sliding mode active disturbance rejection control method with parameter optimization, which specifically includes the following steps: Step 1, establish a mathematical model of a permanent magnet synchronous motor; and construct an extended state observer based on the motor state variables to estimate the system state and total disturbance; Step 2: Construct a cascaded finite-time phase-locked loop (FT-PLLO) observer to perform composite observations on the output of the extended state observer and the disturbance part to obtain the load disturbance estimate and the state error estimate; Step 3: Construct a fractional-order absolute exponential calculus sliding surface to form a sliding mode variable based on the speed error and its fractional integral and fractional derivative terms. Step 4: Construct a PSO-LSTM neural network parameter optimization model. Input the permanent magnet synchronous motor operating status data, error information, and disturbance response data into the LSTM neural network, and optimize the hyperparameters or output parameters of the LSTM neural network using the particle swarm optimization algorithm. Step 5: Traverse and optimize the observer bandwidth using the PSO-LSTM neural network. and controller bandwidth The optimized observer bandwidth Input cascaded FT-PLLO, optimize controller bandwidth The input fractional-order absolute exponential calculus sliding mode controller updates the observer and controller parameters in real time based on the optimized observer and controller bandwidth when the load suddenly increases or decreases, so that the permanent magnet synchronous motor speed tracks the given speed and reduces the transient peak value of electromagnetic torque.

[0019] The composite observation error of a cascaded FT-PLLO includes the improved extended state observer output error and the perturbation component composite observation error, denoted as […]. and .

[0020] The output parameters of the PSO-LSTM neural network include at least the observer bandwidth. and controller bandwidth ,and and Instead of being set as a fixed constant, it is obtained by the PSO-LSTM neural network through traversal, training, and optimization based on the motor operating state and control performance indicators. The control performance indicators include one or more of the following: speed drop, speed overshoot, transient response time, peak electromagnetic torque, electromagnetic torque recovery time, and steady-state error.

[0021] Example 2 The specific process of step 1 is as follows: This invention focuses on three-phase surface-mounted motors (PMSMs). When the rotor structure of a three-phase PMSM differs, its operating performance and control strategy will also vary. This invention focuses on three-phase surface-mounted PMSMs. Figure 1 The diagram shows the main circuit topology of the PMSM. Figure 1 It can be seen that, after Clark and Park transformations, the stator voltage equation of the PMSM in the synchronous rotating coordinate system is: (1) In the formula, u od and u oq These are the stator voltages of the PMSM respectively. d , q Axial components; i od and i oq For PMSM stator current d , q Axial components; R d and R q for d , q Shaft stator resistance; L d and L q for d , q Shaft stator inductance, for surface-mount PMSM, L d and L q They are equal in numerical value; oh e Electric angular velocity; ψ f It is a permanent magnet flux linkage.

[0022] The equations of motion and electromagnetic torque of the PMSM are as follows: (2) In the formula, T e The electromagnetic torque of the PMSM; T l This is the load torque; B The coefficient of friction; J It is the moment of inertia; p n is the number of pole pairs of the PMSM; oh m This refers to the mechanical angular velocity.

[0023] For surface-mount PMSMs, this invention will be based on i d A composite sliding mode active disturbance rejection control strategy with a value of 0 is used to control PMSM.

[0024] Example 3 The specific process of step 2 is as follows: This invention designs an improved sliding mode active disturbance rejection control structure based on the PMSM velocity loop, and the designed cascade FT-PLLO is based on the first-order active disturbance rejection paradigm. The sliding surface part introduces fractional-order theory and designs a variable parameter double power error approaching law to suppress high-frequency chattering when the system state variables approach the sliding surface.

[0025] First, the internal and external disturbances of the system are separated and included in the total disturbance of the system. The corresponding standard first-order active disturbance rejection paradigm is: (3) In the formula, y o This is the system output; u For control input; b 0 represents the controller gain; F v It is the sum of the internal and external disturbances of the separated system.

[0026] This invention designs a sliding mode active disturbance rejection control structure based on the velocity loop of PMSM. Equation (2) is fitted into the standard first-order active disturbance rejection paradigm as follows: (4) In the formula, i oq(ref) For PMSM q Reference value for the inner loop of shaft current.

[0027] Define the state variables of the control system as follows: x 1= oh m ; x 2= F v Based on the defined state variables, its state-space equation is: (5) In the formula, the total internal and external disturbances F v The specific form is: (6) Based on the state-space equation of the system established by equation (5), the first-level structure of the cascaded FT-PLLO can be designed, that is, the form of the linear PLLO is: (7) In the formula, e 11 The observation error is for the first-order linear PLLO. r 11 , r 12 For each linear PLLO, the system state variables are... x 1. x 2 observations; x 11 , x 12 This is the gain coefficient of the linear PLLO.

[0028] Based on the first-level structure of the FT-PLLO established by equation (7), its second-level structure, namely the nonlinear FT-PLLO, can be designed, and its specific form is as follows: (8) In the formula, e 21 This represents the observation error of the second-order nonlinear FT-PLLO. r 21 , r 22 For FT-PLLO, the system state variables are respectively x 1. x 2 observations; x 21 , x 22 tanh is the gain coefficient of FT-PLLO; x ) is the hyperbolic tangent function; 0 < α <1.

[0029] The specific form of the improved ESO established based on equations (7) and (8) is as follows: Figure 2 The diagram shown is the overall structure of a cascaded FT-PLLO.

[0030] according to Figure 2 As shown in the cascaded FT-PLLO structure, due to the large observation error of the first-stage linear PLLO, a second-stage FT-PLLO was designed to further improve its observation accuracy. The designed FT-PLLO treats the perturbation of the linear PLLO as a known part, re-observes it, and finally, this invention outputs the observation values ​​from the second-stage FT-PLLO. r 21 As a state variable x The final observed value of 1.

[0031] Example 4 The specific process of step 4 is as follows: Based on the cascaded FT-PLLO designed in step 3, the input error of the sliding mode controller in the PMSM speed loop can be defined as: (9) In the formula, oh m(ref) This is a reference value for the mechanical angular velocity of the PMSM; r 21 This represents the final observed mechanical angular velocity from the cascaded FT-PLLO.

[0032] Based on the input error of the defined controller, a fractional-order absolute exponential calculus sliding surface is designed. Before designing the sliding surface, the relevant theory of fractional-order calculus is first introduced: (10) In the formula, c Let be the order of the fractional differential operator; l and h These are the lower and upper limits of the fractional integral operator, respectively; Re( c )for c The real part, and c The sign of the real part determines the function f ( t ) is a fractional derivative or fractional integral, when c When the real part is 0, the function f ( t () is of integer order.

[0033] According to the defined fractional order theory, assuming c Since is a real number and is always positive, it is introduced into the original sliding surface to form a fractional-order absolute exponential calculus sliding surface, the specific form of which is: (11) In the formula, e ω Input the rotational speed error for the designed sliding surface; c 1. c 2 represents the sliding surface coefficient; m The design exponent is the absolute exponent term, and 0 < m <1.

[0034] After taking the first derivative of the designed sliding surface and setting it to zero, the equivalent control law of the sliding mode controller can be obtained as follows: (12) Based on the designed fractional-order absolute exponential calculus sliding surface, this invention introduces a variable-parameter double-power error reaching law, specifically in the form of: (13) In the formula, k1 and k2 are the design parameters of the variable parameter double power error approach law, where k1 is greater than 0 and k2 is greater than 1.5; , To improve the high-frequency chattering suppression parameters of the reaching law, and , All are greater than 0; erf(x) is the error function in the probability distribution, and its specific form is: (14) According to the designed variable parameter double power error approaching law, when the system state variable is far from the sliding surface, the coefficient in the first power approaching law takes a larger value to accelerate the speed at which the state variable approaches the sliding surface; when the state variable is close to the sliding surface, the coefficient in the first term takes a smaller value to reduce the high-frequency chattering phenomenon during sliding motion.

[0035] Based on the designed variable-parameter double-power error-reaching law, the specific form of the switching control law in the controller is as follows: (15) According to equations (12) and (15), the overall control law in the PMSM controller is: (16) Based on the fractional-order absolute exponential calculus sliding surface designed by equation (11) and the variable-parameter double-power error reaching law introduced by equation (13), the overall structural block diagram of the controller part is as follows: Figure 3 As shown.

[0036] Example 5 The specific process of step 5 is as follows: A PSO-LSTM neural network model is constructed by inputting the permanent magnet synchronous motor's operating status data, error information, and disturbance response data into the LSTM neural network, and optimizing the hyperparameters or output parameters of the LSTM neural network through the particle swarm optimization algorithm. Step 3.1, build the LSTM neural network, as follows: LSTM (Long Short-Term Memory) neural networks are a special type of recurrent neural network structure, primarily used to process data with time-dependent and sequential characteristics. Compared to traditional RNNs, which are prone to gradient vanishing during training on long sequences of data, LSTMs, by introducing unit states and gating mechanisms, achieve a dynamic process of selectively forgetting historical information, effectively writing current information, and outputting information.

[0037] The core structure of LSTM includes the forget gate, input gate, candidate states, and update unit states, and its mathematical model is as follows: (17) In the formula, f t , i t , c t , u t , o t and h t These are the forget gate, input gate, candidate state, update unit state, output gate, and hidden state output of the LSTM neural network. x t The input vector; h t It is in a hidden state; b f , b i , b c , b o For the offset of the corresponding gate; W f , W i , W c and W o tanh( ) is the weighting coefficient; x ) is the hyperbolic tangent activation function.

[0038] LSTM neural networks utilize their core structure to adjust the degree of retention of old information, the proportion of new information written, and the output strength of the current state.

[13] Its unit structure is as follows: Figure 4 As shown.

[0039] Step 3.2: Optimize the hyperparameters or output parameters of the LSTM neural network using the Particle Swarm Optimization (PSO) algorithm, as follows: Particle Swarm Optimization (PSO) is a global optimization algorithm based on swarm intelligence. It efficiently finds optimal solutions in complex search spaces through information sharing and collaboration among its members. Due to its simple concept, few parameters, and ease of implementation, PSO has been widely applied in function optimization, neural network training, and control system design.

[0040] The basic principle of the PSO algorithm is to represent the potential solutions to the optimization problem as "particles" in the search space, each particle having two attributes: position and velocity. Position represents the specific value of the solution, while velocity determines the direction and distance the particle moves in the search space. The specific form of the velocity update expression in the particle state is: (18) In the formula, i Refers to the first i One particle; v i t For the first i The velocity vector of a particle in space; t This represents the number of iterations in the particle swarm optimization algorithm. oh Inertial weight; c 1. c 2 represents individual and social learning factors, respectively; r 1. r 2. Random numbers sampled independently in each dimension, ranging from [0,1]; P tl The target position for a particle as it traverses space; G tl The target positions for all randomly generated particles to traverse in space; x i t Let be the position vector of a particle in space, and its specific form is: (19) In the formula, x i t+1 For a certain particle in space relative x i t The position vector for the next iteration; This is a constraint factor.

[0041] In particle swarm optimization algorithms, to improve the global search capability of particles in the early stages of iteration, it is also necessary to... oh This inertia factor introduces linear decay, specifically in the form of: (20) In the formula, D This represents the total number of iterations in the particle swarm optimization algorithm. d The current iteration number; the maximum value of the inertia weight. oh max The inertia weight is typically set to 0.9; minimum value. oh min The value is usually 0.3.

[0042] To verify the effectiveness of the particle swarm optimization algorithm, this invention conducted simulation verification. As shown in Figure 5(a), before PSO optimization, 50 dots of different colors are randomly generated in a given square plane, and the target curve is defined as a circle with the center at (0.5, 0.5) and the radius at 0.35.

[0043] This invention introduces a total of 100 particles into the particle swarm optimization algorithm and sets the total number of iterations to 150. These 100 particles are used to optimize the points within a square plane, making them as close as possible to the target curve. Simulation results are shown in Figure 5(b). Most of the optimized points can approach the target curve, demonstrating the superiority of the particle swarm optimization algorithm.

[0044] Since the initial weights and threshold dimensions of the LSTM neural network have a significant impact on its training results, this invention uses the particle swarm optimization algorithm to optimize the LSTM neural network, enabling the LSTM neural network to have higher prediction accuracy for the observer bandwidth, thereby improving the observation accuracy of the designed observer for PMSM rotation speed.

[0045] The principle behind Particle Swarm Optimization (PSO) for optimizing LSTM neural networks is to treat the initial weights and thresholds in the LSTM network as the initial states of each particle in the PSO algorithm, with each particle possessing two attributes: initial position and initial velocity. The iterative training error in the LSTM network is viewed as the target curve or target position in the PSO algorithm. Therefore, the weight adjustment process of the LSTM network can be seen as an optimization process within the PSO algorithm. Optimization through PSO can prevent the LSTM network from getting trapped in local optima. Taking a typical three-layer LSTM neural network as an example, the specific optimization steps are as follows: 1) Select an LSTM neural network and determine the number of hidden layers and the number of neurons between each layer based on its network structure; 2) The total number of iterations in the particle swarm optimization algorithm D Inertia weight oh And set parameters such as the number of particles in PSO; 3) Train the initial weights and threshold of the LSTM neural network using the particle swarm optimization algorithm until the conditions are met; 4) Use the optimal solution in the particle swarm optimization target curve as the initial weights and threshold of the LSTM neural network algorithm; 5) Use the optimal weights and thresholds to iteratively train the LSTM neural network to obtain the optimal observer bandwidth and controller bandwidth; 6) The algorithm ends.

[0046] Based on the above optimization steps, the flowchart of the particle swarm optimization algorithm for optimizing the LSTM neural network is as follows: Figure 6 As shown.

[0047] Observer stability analysis Based on the defined state variables of the system, the composite observation error of the cascaded FT-PLLO is: (twenty one) In the formula, s 1. s 2 represents the improvement of the composite observation error of the ESO output and the perturbation part.

[0048] The specific form of the observation error defined in equation (21) after differentiation is: (twenty two) The following strongly coupled Lyapunov functions are selected: (twenty three) In the formula, V ( s 1, s 2) is the constructed Lyapunov function, which is positive definite and 0 < c <1.

[0049] Differentiating both sides of equation (23) reveals that: (twenty four) Simplify the expression by rearranging like terms and using the two fundamental inequalities: (25) According to the two fundamental inequalities in equation (25), the upper bound of the Lyapunov function is: (26) In the formula, Θ represents the value containing b 0 u , x 2 and d max The cross terms can be designed using gain dominance.

[0050] make x 21 > gx 21 , x 21 > gx 22 Then it exists or >0, such that: (27) Therefore V ( s 1, s 2) The derivative is negative definite and has at most one bounded remainder. d Therefore, the designed cascaded FT-PLLO has stability.

[0051] Controller stability analysis: The fractional Lyapunov candidate function is: (28) In the formula, the introduced Lyapunov function is positive definite and radially unbounded.

[18] .

[0052] Regarding both sides of equation (28) with respect to time t After differentiation, we know that: (29) First, we process the first term in equation (29), and it is easy to see that it exists. β 1>0, such that: (30) Regarding the second term in equation (29), it can be seen from the finite-time convergence of cascaded FT-PLLO that there exists β 3>0 makes: (31) Combining equations (30) and (31), we can see that: (32) Therefore, the designed fractional-order absolute exponential calculus sliding surface possesses asymptotic stability, and the system state variables can achieve asymptotic tracking on the improved sliding surface.

[0053] Example 6 In the simulation section, this invention verifies the simulation results of PMSM under traditional PI control strategy, traditional SMC control strategy and improved control strategy of this invention under sudden load increase and decrease. According to the topology and mathematical model of PMSM system, the circuit parameters of the simulation model are shown in Table 1.

[0054] Table 1 PMSM Circuit Parameters

[0055] in, u dc DC side voltage; R d , R q The stator-side resistance of the PMSM in a synchronous rotating coordinate system; L d , L q Stator-side inductance; ψ f For permanent magnet flux linkage; J , B Here are the moment of inertia and damping coefficient of the PMSM; p n The number of magnetic pole pairs; T s This represents the simulation sampling time.

[0056] The parameters of the improved SM-ADRC controller and PSO-LSTM neural network designed in this invention are shown in Table 2.

[0057] Table 2 Controller and Neural Network Parameters

[0058] In Table 2, oh 0、 oh c These are the observer bandwidth and the controller bandwidth, respectively. Their values ​​are continuously traversed and optimized by the PSO-LSTM neural network and are not fixed values, so they are not given in Table 2.

[0059] The simulation comparison results of rotational speed under sudden load changes are as follows: Figure 7(a) shows the simulated speed waveforms under different control strategies when the load changes abruptly. The given speed is set to 1000 r / min, and the simulation is set so that the load changes from 5 N to 1000 N at 0.3 s. m suddenly increases to 10N m returned to normal in 0.6 seconds.

[0060] As shown in Figure 7(b), when a sudden load increase occurs at 0.3s, the speed under traditional PI (proportional-integral) control drops to 962 r / min with a transient time of 63 ms; while the control effect under SMC (slippery diaphragm) control is improved; when using the control strategy of this invention, that is, when the observer and controller bandwidth are optimized using the PSO-LSTM neural network, the speed under a sudden load increase drops to only 991 r / min with a transient time of only 26 ms. Analysis of Figure 7(c) shows that when the load returns to normal at 0.6s, that is, when a light load occurs, under the control strategy of this invention, the speed under light load increases to only 1004 r / min with a transient time of only 2 ms, which is a significant improvement in control effect compared to the previous two control strategies.

[0061] Electromagnetic torque simulation comparison under sudden load changes Figure 8(a) shows the simulated waveform of the electromagnetic torque, also set at 0.3s with a load of 5N. m suddenly increases to 10N m returned to normal in 0.6 seconds.

[0062] Analysis of Figure 8(b) shows that when the load suddenly increases by 0.3s, the electromagnetic torque under PI control suddenly increases to 16.1N. m, transition time is 14ms; SMC control is an improvement over PI control; under the control of this invention, the electromagnetic torque only increases to 11.3N. m, the time is only 3ms. Analysis of Figure 8(c) shows that when the load returns to normal after 0.6s, the electromagnetic torque controlled by this invention drops to 4N. m, with a time of only 4ms, thus the control strategy of this invention is superior.

[0063] Figure 9 This is the experimental principle of hardware-in-the-loop. To further verify the superiority of the control strategy of this invention, the control structure of PMSM is split into a master topology and a control algorithm, which are then imported into the FPGA and CPU of the hardware-in-the-loop (HIL) system, respectively.

[0064] Figures 10(a) to 10(c) show the experimental results of PMSM speed and electromagnetic torque when the load suddenly increases, starting from 5N. m increases to 10N m, and eventually returned to normal.

[0065] Figure 10(a) shows the experimental results of speed and electromagnetic torque under conventional PI control when the load changes abruptly; Figure 10(b) shows the experimental results of speed and electromagnetic torque under conventional ADRC control when the load changes abruptly; Figure 10(c) shows the experimental results of speed and electromagnetic torque under the control of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention when the load changes abruptly. As shown in Figures 10(a) to 10(c), when the load suddenly increases, the transient peak values ​​of the PMSM electromagnetic torque under conventional PI control, conventional ADRC control, and the control of this invention are 11.4 N, respectively. m, 11.3N m and 11.6N The transient response times of the rotational speed were 37ms, 56ms, and 21ms, respectively, and the transient peak values ​​of the rotational speed were 948 r / min, 972 r / min, and 981 r / min, respectively. When the load returned to normal, the transient peak values ​​of the PMSM electromagnetic torque under different control strategies were 3.4 N. m, 3.5N m and 2.7N The transient response times of the rotational speeds were 32ms, 62ms, and 23ms, respectively, and the transient peak speeds were 1039 r / min, 1023 r / min, and 1019 r / min, respectively. Analysis shows that the control effect of this invention is superior to that of traditional PI control and traditional ADRC control.

[0066] Figures 11(a) to 11(c) show the experimental results of the three-phase stator current of the PMSM when the load suddenly increases, and the load suddenly increases from 5N m increases to 10N m, and eventually returned to normal.

[0067] Figure 11(a) shows the experimental results of the stator three-phase current under conventional PI control when the load changes abruptly; Figure 11(b) shows the experimental results of the stator three-phase current under conventional ADRC control when the load changes abruptly; Figure 11(c) shows the experimental results of the stator three-phase current under the control of the PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization of the present invention when the load changes abruptly.

[0068] Analysis of Figures 11(a) to 11(c) shows that when the load suddenly increases, the transient peak values ​​of the stator three-phase current of the PMSM under traditional PI control, traditional ADRC control, and the control of this invention are 9A, 8A, and 0A, respectively. When the load returns to normal, the transient times of the PMSM stator current under different control methods are 28ms, 14ms, and 6ms, respectively. The analysis shows that the control effect of this invention is superior to the previous two control strategies, further demonstrating the superiority of the control strategy of this invention.

[0069] To address the issues of excessive overshoot and long transient time in speed, electromagnetic torque, and stator current during sudden load changes in PMSM (Power Steering Mode Controller), this invention proposes a composite sliding mode active disturbance rejection control strategy based on a PSO-LSTM neural network to improve the control performance of PMSM. The superiority of the proposed control strategy is verified through simulation and experiments, and the conclusions are as follows: 1) Based on the original structure of the traditional ESO, a cascaded finite-time phase-locked loop observer was designed. Simulation and experiments show that the cascaded FT-PLLO designed in this invention significantly improves the observation accuracy of disturbances.

[0070] 2) Based on the absolute exponential calculus sliding surface, fractional order theory was introduced to finally form a fractional absolute exponential calculus sliding surface. At the same time, a variable parameter double power error approaching law was designed, which significantly suppressed the high-frequency chattering phenomenon when the state variable approached the sliding surface.

[0071] 3) The LSTM neural network optimized by the particle swarm optimization algorithm is used to traverse and optimize the bandwidth of the observer and controller in the improved SM-ADRC of this invention, which greatly improves the control performance of the controller.

Claims

1. A PMSM composite sliding mode active disturbance rejection control method with integrated parameter optimization, characterized in that: Specifically, the steps include the following: Step 1: Establish a mathematical model for the permanent magnet synchronous motor; Step 2: Construct a cascaded finite-time phase-locked observer, i.e., a cascaded FT-PLLO; Step 3: Construct a calculus sliding mode controller; Step 4: Construct the PSO-LSTM neural network optimization model; Step 5: The observer bandwidth and controller bandwidth are traversed and optimized by the PSO-LSTM neural network. The optimized observer bandwidth is input into the cascaded FT-PLLO, and the optimized controller bandwidth is input into the calculus-integral sliding mode controller to realize the control of the permanent magnet synchronous motor.

2. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 1, characterized in that: The specific process of step 1 is as follows: After Clark and Park transformations, the stator voltage equation of the PMSM in the synchronous rotating coordinate system is: （1） In the formula, u od and u oq These are the stator voltages of the PMSM respectively. d , q Axial components; i od and i oq For PMSM stator current d , q Axial components; R d and R q for d , q Shaft stator resistance; L d and L q for d , q Shaft stator inductance, for surface-mount PMSM, L d and L q They are equal in numerical value; ω e Electric angular velocity; ψ f For permanent magnet flux linkage; The equations of motion and electromagnetic torque of the PMSM are as follows: (2) In the formula, T e The electromagnetic torque of the PMSM; T l This is the load torque; B The coefficient of friction; J It is the moment of inertia; p n is the number of pole pairs of the PMSM; ω m This refers to the mechanical angular velocity.

3. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 2, characterized in that: The specific process of step 2 is as follows: Step 2.1, establish the primary structure of FT-PLLO; Step 2.2: Based on the first-level structure of FT-PLLO established in Step 2.1, design the second-level structure, namely the nonlinear FT-PLLO.

4. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 3, characterized in that: The specific process of step 2.1 is as follows: First, the internal and external disturbances of the system are separated and included in the total disturbance of the system. The corresponding standard first-order active disturbance rejection paradigm is: (3) In the formula, y o This is the system output; u For control input; b 0 represents the controller gain; F v This is the sum of the internal and external disturbances of the separated system; Equation (2) is fitted to the standard first-order active disturbance rejection paradigm as follows: (4) In the formula, i oq(ref) For PMSM q Reference value for the inner loop of shaft current; Define the state variables of the control system as follows: x 1= ω m ; x 2= F v Based on the defined state variables, the state-space equation is: (5) In the formula, the total internal and external disturbances F v The specific form is: (6) Based on the state-space equation of the system established by equation (5), the first-level structure of the cascaded FT-PLLO can be designed, that is, the form of the linear PLLO is: (7) In the formula, e 11 The observation error is for the first-order linear PLLO. ρ 11 , ρ 12 For each linear PLLO, the system state variables are... x 1. x 2 observations; ξ 11 , ξ 12 This is the gain coefficient of the linear PLLO.

5. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 4, characterized in that: The specific process of step 2.2 is as follows: Based on the first-level structure of the FT-PLLO established by equation (7), a second-level structure, namely the nonlinear FT-PLLO, is designed, with the following specific form: (8) In the formula, e 21 This represents the observation error of the second-order nonlinear FT-PLLO. ρ 21 , ρ 22 For FT-PLLO, the system state variables are respectively x 1. x 2 observations; ξ 21 , ξ 22 tanh is the gain coefficient of FT-PLLO; x ) is the hyperbolic tangent function; 0 < α <1.

6. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 5, characterized in that: The specific process of step 3 is as follows: The input error of the sliding mode controller in the PMSM speed loop is defined as: (9) In the formula, ω m(ref) This is a reference value for the mechanical angular velocity of the PMSM; ρ 21 This represents the final observation of the mechanical angular velocity by the cascaded FT-PLLO; Based on the input error of the defined controller, a fractional-order absolute exponential calculus sliding surface is designed. First, the fractional-order formula is introduced as follows: (10) In the formula, γ Let be the order of the fractional differential operator; l and h These are the lower and upper limits of the fractional integral operator, respectively; Re( γ )for γ The real part, and γ The sign of the real part determines the function f ( t ) is a fractional derivative or fractional integral, when γ When the real part is 0, the function f ( t () is of integer order; According to the defined fractional order theory, assuming γ Given a real number that is always positive, it is introduced into the designed original sliding surface to form a fractional-order absolute exponential calculus sliding surface, specifically in the form of: (11) In the formula, ε ω Input the rotational speed error for the designed sliding surface; c 1. c 2 represents the sliding surface coefficient; μ The design exponent is the absolute exponent term, and 0 < μ <1.

7. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 5, characterized in that: In step 3, after calculating the first derivative of the designed sliding surface, the derivative result is set to zero, and the equivalent control law of the sliding controller is obtained as follows: (12) Based on the designed fractional-order absolute exponential calculus sliding surface, a variable-parameter double-power error reaching law is introduced, specifically in the form of: (13) In the formula, k1 and k2 are the design parameters of the variable parameter double power error approach law, where k1 is greater than 0 and k2 is greater than 1.5; , To improve the high-frequency chattering suppression parameters of the reaching law, and , All are greater than 0; erf(x) is the error function in the probability distribution, specifically in the form of: (14) Based on the designed variable-parameter double-power error-reaching law, the specific form of the switching control law in the controller is as follows: (15) According to equations (12) and (15), the overall control law in the PMSM controller is: (16)。 8. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 7, characterized in that: The specific process of step 4 is as follows: Step 4.1, establish the mathematical model of LSTM, specifically as follows: (17) In the formula, f t , i t , c t , u t , o t and h t These are the forget gate, input gate, candidate state, update unit state, output gate, and hidden state output of the LSTM neural network. x t The input vector; h t It is in a hidden state; b f , b i , b c , b o For the offset of the corresponding gate; W f , W i , W c and W o tanh( ) is the weighting coefficient; x ) is the hyperbolic tangent activation function; Step 4.2: Optimize the hyperparameters or output parameters of the LSTM neural network using the Particle Swarm Optimization (PSO) algorithm to obtain the PSO-LSTM neural network parameter optimization model.

9. The PMSM composite sliding mode active disturbance rejection control method with fused parameter optimization according to claim 8, characterized in that: The specific process of step 4.2 is as follows: The specific form of the velocity update expression in the particle state is: (18) In the formula, i Refers to the first i One particle; v i t For the first i The velocity vector of a particle in space; t This represents the number of iterations in the particle swarm optimization algorithm. ω Inertial weight; c 1. c 2 represents individual and social learning factors, respectively; r 1. r 2. Random numbers sampled independently in each dimension, ranging from [0,1]; P tl The target position for a particle as it traverses space; G tl The target positions for all randomly generated particles to traverse in space; x i t Let be the position vector of a particle in space, specifically in the form of: (19) In the formula, x i t+1 For a certain particle in space relative x i t The position vector for the next iteration; Constraint factors; In the ω This inertia factor introduces linear decay, specifically in the form of: (20) In the formula, D This represents the total number of iterations in the particle swarm optimization algorithm. d This represents the current iteration number; ω max This represents the maximum value of the inertia weight. ω min This represents the minimum inertial weight.

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